Fractional Iteration of Series and Transseries

We investigate compositional iteration of fractional order for transseries. For any large positive transseries $T$ of exponentiality 0, there is a family $T^{[s]}$ indexed by real numbers $s$ corresponding to teration of order $s$. It is based on Abel's Equation. We also investigate the question of whether there is a family $T^{[s]}$ all sharing a single support set. A subset of the transseries of exponentiality 0 is divided into three classes ("shallow", "moderate" and "deep") with different properties related to fractional iteration.Comment: 17 pages; 1 figur

Computational wing design studies relating to natural laminar flow

Two research studies are described which directly relate to the application of natural laminar flow (NLF) technology to transonic transport-type wing planforms. Each involved using state-of-the-art computational methods to design three-dimensional wing contours which generate significant runs of favorable pressure gradients. The first study supported the Variable Sweep Transition Flight Experiment and involves design of a full-span glove which extends from the leading edge to the spoiler hinge line on the upper surface of an F-14 outer wing panel. A wing was designed computationally for a corporate transport aircraft in the second study. The resulting wing design generated favorable pressure gradients from the leading edge aft to the mid-chord on both upper and lower surfaces at the cruise design point. Detailed descriptions of the computational design approach are presented along with the various constraints imposed on each of the designs

Probing double parton scattering via associated open charm and bottom production in ultraperipheral pApA collisions

In this article, we propose a novel channel for phenomenological studies of the double-parton scattering (DPS) based upon associated production of charm $c\bar{c}$ and bottom $b\bar{b}$ quark pairs in well-separated rapidity intervals in ultra-peripheral high-energy proton-nucleus collisions. This process provides a direct access to the double-gluon distribution in the proton at small-$x$ and enables one to test the factorised DPS pocket formula. We have made the corresponding theoretical predictions for the DPS contribution to this process at typical LHC energies and beyond and we compute the energy-independent (but photon momentum fraction dependent) effective cross section.Comment: 15 pages, 7 figs., 1 table. One fig. added. Version accepted for publication at EPJ